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y-values in the solution to x^2-53*y^2=1.
2

%I #16 Sep 08 2022 08:45:51

%S 0,9100,1205731800,159757052027300,21167489878307463600,

%T 2804650073736225260045500,371610525448734884627201195400,

%U 49237651398101824669598678728063700,6523890334574085039623750849483782927200

%N y-values in the solution to x^2-53*y^2=1.

%C The corresponding values of x of this Pell equation are in A174757.

%H Vincenzo Librandi, <a href="/A174983/b174983.txt">Table of n, a(n) for n = 1..200</a>

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (132498,-1).

%F a(n) = 132498*a(n-1)-a(n-2) with a(1)=0, a(2)=9100.

%F G.f.: 9100*x^2/(1-132498*x+x^2).

%t LinearRecurrence[{132498,-1},{0,9100},30]

%o (Magma) I:=[0, 9100]; [n le 2 select I[n] else 132498*Self(n-1)-Self(n-2): n in [1..20]];

%Y Cf. A174757

%K nonn,easy

%O 1,2

%A _Vincenzo Librandi_, Apr 15 2010